C++ Bignum::pow_mod方法代码示例

bool CommitmentProofOfKnowledge::Verify(const Bignum& A, const Bignum& B) const
{
    // TODO: First verify that the values
    // S1, S2 and S3 and "challenge" are in the correct ranges
    if((this->challenge < Bignum(0)) || (this->challenge > (Bignum(2).pow(256) - Bignum(1)))){
        return false;
    }
    
    // Compute T1 = g1^S1 * h1^S2 * inverse(A^{challenge}) mod p1
    Bignum T1 = A.pow_mod(this->challenge, ap->modulus).inverse(ap->modulus).mul_mod(
                                                                         (ap->g.pow_mod(S1, ap->modulus).mul_mod(ap->h.pow_mod(S2, ap->modulus), ap->modulus)),
                                                                         ap->modulus);
    
    // Compute T2 = g2^S1 * h2^S3 * inverse(B^{challenge}) mod p2
    Bignum T2 = B.pow_mod(this->challenge, bp->modulus).inverse(bp->modulus).mul_mod(
                                                                         (bp->g.pow_mod(S1, bp->modulus).mul_mod(bp->h.pow_mod(S3, bp->modulus), bp->modulus)),
                                                                         bp->modulus);
    
    // Hash T1 and T2 along with all of the public parameters
    Bignum computedChallenge = calculateChallenge(A, B, T1, T2);
    
    // Return success if the computed challenge matches the incoming challenge
    if(computedChallenge == this->challenge){
        return true;
    }
    
    // Otherwise return failure
    return false;
}

/** Verifies that a commitment c is accumulated in accumulator a
 */
bool AccumulatorProofOfKnowledge:: Verify(const Accumulator& a, const Bignum& valueOfCommitmentToCoin) const {
	Bignum sg = params->accumulatorPoKCommitmentGroup.g;
	Bignum sh = params->accumulatorPoKCommitmentGroup.h;

	Bignum g_n = params->accumulatorQRNCommitmentGroup.g;
	Bignum h_n = params->accumulatorQRNCommitmentGroup.h;

	//According to the proof, this hash should be of length k_prime bits.  It is currently greater than that, which should not be a problem, but we should check this.
	CHashWriter hasher(0,0);
	hasher << *params << sg << sh << g_n << h_n << valueOfCommitmentToCoin << C_e << C_u << C_r << st_1 << st_2 << st_3 << t_1 << t_2 << t_3 << t_4;

	Bignum c = Bignum(hasher.GetHash()); //this hash should be of length k_prime bits

	Bignum st_1_prime = (valueOfCommitmentToCoin.pow_mod(c, params->accumulatorPoKCommitmentGroup.modulus) * sg.pow_mod(s_alpha, params->accumulatorPoKCommitmentGroup.modulus) * sh.pow_mod(s_phi, params->accumulatorPoKCommitmentGroup.modulus)) % params->accumulatorPoKCommitmentGroup.modulus;
	Bignum st_2_prime = (sg.pow_mod(c, params->accumulatorPoKCommitmentGroup.modulus) * ((valueOfCommitmentToCoin * sg.inverse(params->accumulatorPoKCommitmentGroup.modulus)).pow_mod(s_gamma, params->accumulatorPoKCommitmentGroup.modulus)) * sh.pow_mod(s_psi, params->accumulatorPoKCommitmentGroup.modulus)) % params->accumulatorPoKCommitmentGroup.modulus;
	Bignum st_3_prime = (sg.pow_mod(c, params->accumulatorPoKCommitmentGroup.modulus) * (sg * valueOfCommitmentToCoin).pow_mod(s_sigma, params->accumulatorPoKCommitmentGroup.modulus) * sh.pow_mod(s_xi, params->accumulatorPoKCommitmentGroup.modulus)) % params->accumulatorPoKCommitmentGroup.modulus;

	Bignum t_1_prime = (C_r.pow_mod(c, params->accumulatorModulus) * h_n.pow_mod(s_zeta, params->accumulatorModulus) * g_n.pow_mod(s_epsilon, params->accumulatorModulus)) % params->accumulatorModulus;
	Bignum t_2_prime = (C_e.pow_mod(c, params->accumulatorModulus) * h_n.pow_mod(s_eta, params->accumulatorModulus) * g_n.pow_mod(s_alpha, params->accumulatorModulus)) % params->accumulatorModulus;
	Bignum t_3_prime = ((a.getValue()).pow_mod(c, params->accumulatorModulus) * C_u.pow_mod(s_alpha, params->accumulatorModulus) * ((h_n.inverse(params->accumulatorModulus)).pow_mod(s_beta, params->accumulatorModulus))) % params->accumulatorModulus;
	Bignum t_4_prime = (C_r.pow_mod(s_alpha, params->accumulatorModulus) * ((h_n.inverse(params->accumulatorModulus)).pow_mod(s_delta, params->accumulatorModulus)) * ((g_n.inverse(params->accumulatorModulus)).pow_mod(s_beta, params->accumulatorModulus))) % params->accumulatorModulus;

	bool result = false;

	bool result_st1 = (st_1 == st_1_prime);
	bool result_st2 = (st_2 == st_2_prime);
	bool result_st3 = (st_3 == st_3_prime);

	bool result_t1 = (t_1 == t_1_prime);
	bool result_t2 = (t_2 == t_2_prime);
	bool result_t3 = (t_3 == t_3_prime);
	bool result_t4 = (t_4 == t_4_prime);

	bool result_range = ((s_alpha >= -(params->maxCoinValue * Bignum(2).pow(params->k_prime + params->k_dprime + 1))) && (s_alpha <= (params->maxCoinValue * Bignum(2).pow(params->k_prime + params->k_dprime + 1))));

	result = result_st1 && result_st2 && result_st3 && result_t1 && result_t2 && result_t3 && result_t4 && result_range;

	return result;
}

Bignum
generateRandomPrime(uint32_t primeBitLen, uint256 in_seed, uint256 *out_seed,
                    uint32_t *prime_gen_counter)
{
	// Verify that primeBitLen is not too small
	if (primeBitLen < 2) {
		throw ZerocoinException("Prime length is too short");
	}

	// If primeBitLen < 33 bits, perform the base case.
	if (primeBitLen < 33) {
		Bignum result(0);

		// Set prime_seed = in_seed, prime_gen_counter = 0.
		uint256     prime_seed = in_seed;
		(*prime_gen_counter) = 0;

		// Loop up to "4 * primeBitLen" iterations.
		while ((*prime_gen_counter) < (4 * primeBitLen)) {

			// Generate a pseudorandom integer "c" of length primeBitLength bits
			uint32_t iteration_count;
			Bignum c = generateIntegerFromSeed(primeBitLen, prime_seed, &iteration_count);
#ifdef ZEROCOIN_DEBUG
			cout << "generateRandomPrime: primeBitLen = " << primeBitLen << endl;
			cout << "Generated c = " << c << endl;
#endif

			prime_seed += (iteration_count + 1);
			(*prime_gen_counter)++;

			// Set "intc" to be the least odd integer >= "c" we just generated
			uint32_t intc = c.getulong();
			intc = (2 * floor(intc / 2.0)) + 1;
#ifdef ZEROCOIN_DEBUG
			cout << "Should be odd. c = " << intc << endl;
			cout << "The big num is: c = " << c << endl;
#endif

			// Perform trial division on this (relatively small) integer to determine if "intc"
			// is prime. If so, return success.
			if (primalityTestByTrialDivision(intc)) {
				// Return "intc" converted back into a Bignum and "prime_seed". We also updated
				// the variable "prime_gen_counter" in previous statements.
				result = intc;
				*out_seed = prime_seed;

				// Success
				return result;
			}
		} // while()

		// If we reached this point there was an error finding a candidate prime
		// so throw an exception.
		throw ZerocoinException("Unable to find prime in Shawe-Taylor algorithm");

		// END OF BASE CASE
	}
	// If primeBitLen >= 33 bits, perform the recursive case.
	else {
		// Recurse to find a new random prime of roughly half the size
		uint32_t newLength = ceil((double)primeBitLen / 2.0) + 1;
		Bignum c0 = generateRandomPrime(newLength, in_seed, out_seed, prime_gen_counter);

		// Generate a random integer "x" of primeBitLen bits using the output
		// of the previous call.
		uint32_t numIterations;
		Bignum x = generateIntegerFromSeed(primeBitLen, *out_seed, &numIterations);
		(*out_seed) += numIterations + 1;

		// Compute "t" = ⎡x / (2 * c0⎤
		// TODO no Ceiling call
		Bignum t = x / (Bignum(2) * c0);

		// Repeat the following procedure until we find a prime (or time out)
		for (uint32_t testNum = 0; testNum < MAX_PRIMEGEN_ATTEMPTS; testNum++) {

			// If ((2 * t * c0) + 1 > 2^{primeBitLen}),
			// then t = ⎡2^{primeBitLen} – 1 / (2 * c0)⎤.
			if ((Bignum(2) * t * c0) > (Bignum(2).pow(Bignum(primeBitLen)))) {
				t = ((Bignum(2).pow(Bignum(primeBitLen))) - Bignum(1)) / (Bignum(2) * c0);
			}

			// Set c = (2 * t * c0) + 1
			Bignum c = (Bignum(2) * t * c0) + Bignum(1);

			// Increment prime_gen_counter
			(*prime_gen_counter)++;

			// Test "c" for primality as follows:
			// 1. First pick an integer "a" in between 2 and (c - 2)
			Bignum a = generateIntegerFromSeed(c.bitSize(), (*out_seed), &numIterations);
			a = Bignum(2) + (a % (c - Bignum(3)));
			(*out_seed) += (numIterations + 1);

			// 2. Compute "z" = a^{2*t} mod c
			Bignum z = a.pow_mod(Bignum(2) * t, c);

			// 3. Check if "c" is prime.
			//    Specifically, verify that gcd((z-1), c) == 1 AND (z^c0 mod c) == 1
//.........这里部分代码省略.........